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His father's remarkable life, in particular, has shaped his own narrative. "He was born in Samoa, but he didn't know his own dad," Parker revealed. "He was one of 27 or 28 kids and my mum is one of 26.
"When he was a baby someone stood on his leg and that's why he can't box. One leg is skinnier than the other leg. But he had a lot of street fights, and if he had a good leg he'd be taller than me.
"His whole life he was treated pretty bad. He lived out in the bush until he was 27, hunting for food like a real bush man - he had a big beard as well. He was surviving on bats and eels and berries. But all that made him stronger. Then he came to New Zealand and had his own family.
"He's told me all about it and everyone in the family has told me how hard his life was. And every time they tell me they get emotional. A big part of all this is for dad. I want him to see his son being successful."
Parker clearly owes much to his father, not least his stoicism. Dempsey took him on the pads at home when he was just four years old; eight years later, it was time to take things up a notch.
"I was walking home from school and was followed home by these guys from another school," Parker recalled. "I went home and my dad said: 'What are these guys doing here?' I said they followed me home and wanted to fight with me. He told me to take off my shirt, drop my bag and go to the front of the house and fight. I was 12 and the other boy was 16.
"I'd never fought on the street before. I got beat up a bit. He told my mum when she got home that I tripped up and fell. I had blood all over my face. I had just started training. He was testing me."
From these brutal beginnings, Parker has now well and truly arrived. Sunday's meeting with Joshua is the chance to etch himself into the record books, although he is motivated by more than just personal glory.
Join the Herald's live blog of Parker v Joshua from 8am Sunday
Becoming New Zealand's first heavyweight champion in 2016 by winning the WBO title in Auckland was - as he puts it - "for the whole of New Zealand. I was proud to be a New Zealand Samoan and put them on the map. Now we've got the opportunity to unify the belts and that's pretty amazing.
"I think it's in our blood. We're a warrior nation. It's part of the culture. But we only want to fight if it means something."
This fight certainly does. Parker stands to earn £7 million (NZ$13.6m) for his efforts and should treble that in the event of a rematch if he wins.
He has met Joshua socially once before, at the Azerbaijan World Championships in 2011, with the Briton going on to win a silver medal.
It was a significant moment for Parker, who decided to leave New Zealand and make his home in Las Vegas to work alongside Kevin Barrie, now his mentor.
"I always believed I'd be world champion, I just didn't know when," he said. "My dad believed it as well. There's a reason why I'm down this path.
"I'm prepared for one of the biggest fights I'll be involved in. Everyone says you're going to have stage fright and be nervous walking out in front of so many people but I'm so blessed and grateful to have a team around me who keep me grounded."
Focused, too. There has been little of the trash-talk which so often accompanies big fights; instead, Parker is quietly respectful of Joshua, as a fighter and a man.
"He's similar to me - a gentleman. Very respectful. He knows how to handle himself and he has been through this before. He's very experienced and he has confidence. We both respect each other and compliment each other but we know what we want."
Just before his lonely walk to the ring on Saturday night, he will - as always - embrace his parents, and think of the reason he is putting himself through all this.
"What I wanted as a young boy was to look after my family, because of the hard work they have put into me. So I want to buy a home for my parents. Just a normal home. I want to help everyone who has looked after me and helped me."
